Five friends Alastair, Bell, Cook, Darren and Eoin appeared

Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

The OA is D.

Quote

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Tue Aug 21, 2018 10:49 pm

BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

The OA is D.

Say the scores of Alastair, Bell, Cook, Darren and Eoin are a, b, c, d, and e, respectively.

Thus, from the given information, we have

d = c + 1/5 of c = 6c/5
a = d/2 = 3c/5
e = c + 2/5 of c = 7c/5

d = 3b/2
=> b = 2d/3 = 2/3*(6c/5) = 4c/5

Given, the average score (arithmetic mean) of the group was 50, the total score of all the five students = 5*50 = 250

Thus, a + b + c + d + e = 250

3c/5 + 4c/5 + c + 6c/5 + 7c/5 = 250

=> c = 50

We see that the highest score is 7c/5 = 7/5*50 = 70 and the smallest score is 3c/5 = 3/5*50 = 30

Thus, the range = 70 - 30 = 40.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Jayanagar | GMAT Prep Jayanagar | GRE Prep Madhapur | Kukatpally GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Aug 22, 2018 2:57 am

BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

To determine the ratio of the scores, plug in numbers and reduce the resulting ratio as much as possible.
Let A = Alastair, B = Bell, C = Cook, D = Darren, and E = Eoin.
Let B = the product of the denominators = 2*5*5*2 = 100.

Darren's score was 3/2 times that of Bell's score.
D = 3/2(B) = (3/2)(100) = 150.

Alastair scored exactly 1/2 of Darren's score.
A = (1/2)D = (1/2)(150) = 75.

Darren's score was 1/5th more than Cook's score.
In other words, Darren's score of 150 is 6/5 Cook's score:
150 = (6/5)C
C = (5/6)150 = 125.

Eoin scored 2/5th more than Cook.
In other words, Eoin's score is 7/5 Cook's score of 125:
E = (7/5)125 = 175.

A : B : C : D : E = 75

125:150:175 = 3:4:5:6:7.
When the values in the ratio are fully reduced, biggest - smallest = 7-3 = 4.
Implication:
The range of the values must be a MULTIPLE OF 4.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 7244; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Aug 23, 2018 4:10 pm

BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

Let's let Cook's score be x.

Since Darren's score is 1/5th more than Cook's; Darren's score must be x + (x/5) = 6x/5.

Since Alastair's score is 1/2 of Darren's, Alastair's score is (6x/5)(1/2) = 3x/5.

Since Eoin's score is 2/5th more than Cook's; Eoin's score is x + (2x/5) = 7x/5.

Finally, since Darren's score is 3/2 times Bell's score; Bells score is (6x/5)/(3/2) = 4x/5.

Since the average score of the group is 50, the sum of their scores is 50 * 5 = 250.

We can set up the following equation:

3x/5 + 4x/5 + x + 6x/5 + 7x/5 = 250

25x/5 = 250

5x = 250

x = 50

So, the lowest score was 3(50)/5 = 30 and the highest score was 7(50)/5 = 70. The range is 70 - 30 = 40.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Quote

Post new topic Post Reply

• Page 1 of 1

5/5

5 Star (473 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review